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13
SMTbased bisimulation minimisation of markov models
 In VMCAI, volume 7737 of LNCS
, 2013
"... Abstract. Probabilistic model checking is an increasingly widely used formal verification technique. However, its dependence on computationally expensive numerical operations makes it particularly susceptible to the statespace explosion problem. Among other abstraction techniques, bisimulation min ..."
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Abstract. Probabilistic model checking is an increasingly widely used formal verification technique. However, its dependence on computationally expensive numerical operations makes it particularly susceptible to the statespace explosion problem. Among other abstraction techniques, bisimulation minimisation has proven to shorten computation times significantly, but, usually, the full state space needs to be built prior to minimisation. We present a novel approach that leverages satisfiability solvers to extract the minimised system from a highlevel description directly. A prototypical implementation in the framework of the probabilistic model checker Prism provides encouraging experimental results. 1
Compositional Approach to Suspension and Other Improvements to LTL Translation
"... Recently, there was defined a fragment of LTL (containing fairness properties among other interesting formulae) whose validity over a given infinite word depends only on an arbitrary suffix of the word. Building upon an existing translation from LTL to Büchi automata, we introduce a compositional ..."
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Recently, there was defined a fragment of LTL (containing fairness properties among other interesting formulae) whose validity over a given infinite word depends only on an arbitrary suffix of the word. Building upon an existing translation from LTL to Büchi automata, we introduce a compositional approach where subformulae of this fragment are translated separately from the rest of an input formula and the produced automata are composed in a way that the subformulae are checked only in relevant accepting strongly connected components of the final automaton. Further, we suggest improvements over some procedures commonly applied to generalized Büchi automata, namely over generalized acceptance simplification and over degeneralization. Finally we show how existing simulationbased reductions can be implemented in a signaturebased framework in a way that improves the determinism of the automaton.
Symbolic partition refinement with dynamic balancing of time and space
 In QEST
"... Bisimulation minimization is one of the classical means to fight the infamous state space explosion problem in verification. Particularly in stochastic verification, numerical algorithms are applied, which do not scale beyond systems of moderate size. To alleviate this problem, symbolic bisimulation ..."
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Bisimulation minimization is one of the classical means to fight the infamous state space explosion problem in verification. Particularly in stochastic verification, numerical algorithms are applied, which do not scale beyond systems of moderate size. To alleviate this problem, symbolic bisimulation minimization has been used effectively to reduce very large symbolically represented state spaces to moderate size explicit representations. But even this minimization may fail due to time or memory limitations. This paper presents a symbolic algorithm which relies on a hybrid symbolic partition representation. It dynamically converts between two known representations in order to provide a tradeoff between memory consumption and runtime. The conversion itself is logarithmic in the partition size. We show how to apply it for the minimization of Markov chains, but the same techniques can be adapted in a straightforward way to other models like labeled transition systems or interactive Markov chains. 1
Correctness Issues of Symbolic Bisimulation Computation for Markov Chains ⋆
"... Abstract. Bisimulation reduction is a classical means to fight the infamous state space explosion problem, which limits the applicability of automated methods for verification like model checking. A signaturebased method, originally developed by Blom and Orzan for labeled transition systems and ada ..."
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Abstract. Bisimulation reduction is a classical means to fight the infamous state space explosion problem, which limits the applicability of automated methods for verification like model checking. A signaturebased method, originally developed by Blom and Orzan for labeled transition systems and adapted for Markov chains by Derisavi, has proved to be very efficient. It is possible to implement it symbolically using binary decision diagrams such that it is able to handle very large state spaces efficiently. We will show, however, that for Markov chains this algorithm suffers from numerical instabilities, which often result in too large quotient systems. We will present and experimentally evaluate two different approaches to avoid these problems: first the usage of rational arithmetic, and second an approach not only to represent the system structure but also the transition rates symbolically. In addition, this allows us to modify their actual values after the quotient computation. 1
Forwarding, Splitting, and Block Ordering to Optimize BDDbased Bisimulation Computation
, 2007
"... In this paper we present optimizations for a BDDbased algorithm for the computation of several types of bisimulations which play an important role for minimisation of large systems thus enabling their verification. The basic principle of the algorithm is partition refinement. Our proposed optimizat ..."
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In this paper we present optimizations for a BDDbased algorithm for the computation of several types of bisimulations which play an important role for minimisation of large systems thus enabling their verification. The basic principle of the algorithm is partition refinement. Our proposed optimizations take this refinementstructure as well as the usage of BDDs for the representation of the system into account: (1) block forwarding updates insitu newly refined blocks of the partition, (2) splitdriven refinement approximates the blocks that may be refined, and (3) block ordering heuristically suggests a good order in which the blocks will be refined. We provide substantial experimental results on examples from different applications and compare them to alternative approaches. The experiments clearly show that the proposed optimization techniques result in a significant performance speedup compared to the basic algorithm as well as to alternative approaches.
On the Minimisation of Acyclic Models ⋆
"... Abstract. This paper presents a novel algorithm to compute weak bisimulation quotients for finite acyclic models. It is developed in the setting of interactive Markov chains, a model overarching both labelled transition systems and continuoustime Markov chains. This model has lately been used to gi ..."
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Abstract. This paper presents a novel algorithm to compute weak bisimulation quotients for finite acyclic models. It is developed in the setting of interactive Markov chains, a model overarching both labelled transition systems and continuoustime Markov chains. This model has lately been used to give an acyclic compositional semantics to dynamic fault trees, a reliability modelling formalism. While the theoretical complexity does not change substantially, the algorithm performs very well in practice, almost linear in the size of the input model. We use a number of case studies to show that it is vastly more efficient than the standard bisimulation minimisation algorithms. In particular we show the effectiveness in the analysis of dynamic fault trees. 1
Cost preserving bisimulations for probabilistic automata
 In CONCUR, volume 8052 of LNCS
, 2013
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On Abstraction of Probabilistic Systems
"... Abstract. Probabilistic model checking extends traditional model checking by incorporating quantitative information about the probability of system transitions. However, probabilistic models that describe interesting behavior are often too complex for straightforward analysis. Abstraction is one ..."
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Abstract. Probabilistic model checking extends traditional model checking by incorporating quantitative information about the probability of system transitions. However, probabilistic models that describe interesting behavior are often too complex for straightforward analysis. Abstraction is one way to deal with this complexity: instead of analyzing the (“concrete”) model, a simpler (“abstract”) model that preserves the relevant properties is built and analyzed. This paper surveys various abstraction techniques proposed in the past decade. For each abstraction technique we identify in what sense properties are preserved or provide alternatively suitable boundaries. 1